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This paper provides an exact simulation algorithm for the sampling from thejoint law of the first-passage time, the undershoot and the overshoot of asubordinator crossing a non-increasing boundary. We prove that the running timeof this algorithm has finite moments of all positive orders and give anexplicit bound on the expected running time in terms of the L\'evy measure ofthe subordinator. This bound provides performance guarantees that make ouralgorithm suitable for Monte Carlo estimation. We provide a GitHub repositorywith an implementation of the algorithm in Python and Julia.

Fast exact simulation of the first-passage event of a subordinator